Stochastic-Adversarial Channels: Online Adversaries With Feedback Snooping

The growing need for reliable communication over untrusted networks has caused a renewed interest in adversarial channel models, which often behave much differently than traditional stochastic channel models. Of particular practical use is the assumption of a causal or online adversary who is limited to causal knowledge of the transmitted codeword. In this work, we consider stochastic-adversarial mixed noise models. In the setup considered, a transmit node (Alice) attempts to communicate with a receive node (Bob) over a binary erasure channel (BEC) or binary symmetric channel (BSC) in the presence of an online adversary (Calvin) who can erase or flip up to a certain number of bits at the input of the channel. Calvin knows the encoding scheme and has strict causal access to Bob's reception through feedback snooping. For erasures, we provide a complete capacity characterization with and without transmitter feedback. For bit-flips, we provide converse and achievability bounds.